Miller has been meeting with key GOP senators and conservative groups to discuss his chances. Among the senators who have chatted with him are Rand Paul of Kentucky, Ron Johnson of Wisconsin, and Kansas Sen. Jerry Moran, chairman of the National Republican Senatorial Committee (NRSC).

Miller has also conferred with former South Carolina Sen. Jim DeMint, president of The Heritage Foundation, according to Politico.

If he runs Miller can expect some stiff competition, not just from Democrats but from his own party. Lt. Gov. Mead Treadwell has already declared his in interest in running for the GOP Senate nomination, and supporters of Gov. Sean Parnell are waiting to see if he'll run as well.

And then there's always the possibility that Miller could get into a skirmish with GOP political strategist Karl Rove, whose Conservative Victory Project PAC is challenging Republican candidates it views as too extreme to carry the party's conservative banner. A spokesman for the PAC told Politico that it has no stance on the Alaska races yet.

Asked about Miller's possible candidacy, Moran told Politico that the goal of the NRSC is to "sit down with folks in Alaska and see if we can have that dialogue about who is the best candidate that can win.

"But that’s a decision to be made in Alaska, and not in Washington, D.C.,” he added. "The goal is to see if we can avoid spending all of our resources fighting and arguing among Republicans."